instead of a tear away use a stay in stablizer- even muslin foundation works well- if you are sticking with the tear away you should not remove any of it until the quilt top is together- or at least each block is attached to what it will be attached to.
stitch carefully on the lines with a shorter stitch length than usually used in piecing. anytime doing paper/foundation piecing you need a shorter stitch length.
when you flip each piece after stitching simply finger press it-carefully without distorting it. wait until the block is finished before pressing- then simply put the iron down and pick it up- do not iron across your block- another way of distorting it- press- don't iron-